Open Access
March 2010 Stein’s method and Normal approximation of Poisson functionals
G. Peccati, J. L. Solé, M. S. Taqqu, F. Utzet
Ann. Probab. 38(2): 443-478 (March 2010). DOI: 10.1214/09-AOP477


We combine Stein’s method with a version of Malliavin calculus on the Poisson space. As a result, we obtain explicit Berry–Esséen bounds in Central limit theorems (CLTs) involving multiple Wiener–Itô integrals with respect to a general Poisson measure. We provide several applications to CLTs related to Ornstein–Uhlenbeck Lévy processes.


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G. Peccati. J. L. Solé. M. S. Taqqu. F. Utzet. "Stein’s method and Normal approximation of Poisson functionals." Ann. Probab. 38 (2) 443 - 478, March 2010.


Published: March 2010
First available in Project Euclid: 9 March 2010

zbMATH: 1195.60037
MathSciNet: MR2642882
Digital Object Identifier: 10.1214/09-AOP477

Primary: 60F05 , 60G51 , 60G60 , 60H05

Keywords: Malliavin calculus , Normal approximation , Ornstein–Uhlenbeck process , Poisson measure , Stein’s method , Wasserstein distance

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 2 • March 2010
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